We propose a model for learning user preference rankings for the purpose of
making product recommendations. The model allows us to learn from pairwise
preference statements or from (incomplete) rankings over more than two items. We
present two algorithms for performing inference in this model, both with
excellent scaling in the number of users and items. The superior predictive
performance of the new method is demonstrated on the well-known sushi preference
data set. In addition, we show how the model can be used effectively in an active
learning setting where we select only a small number of informative items for
learning.